What is the smallest integer value of x that satisfies both x > -3 and 2x - 7 > 5?

Solve the second inequality: $2x - 7 > 5$ gives $2x > 12$, so $x > 6$. The first inequality, $x > -3$, is weaker, because any number greater than 6 is automatically greater than $-3$. The combined solution is $x > 6$. The smallest integer greater than 6 is 7. Notice that 6 itself does not work, since $2(6) - 7 = 5$, which is not greater than 5. A common wrong answer is 6, from treating the inequality as non-strict. Another is $-2$, the smallest integer satisfying only the first inequality. Both conditions must hold.